https://orcid.org/0000-0001-6978-2619
Abstract
This paper proposes an offset-free Quasi-Infinite Horizon Nonlinear Model Predictive Controller (QIH-NMPC) using online parameter adaptation. In the proposed method, the adaptation law is modeled by a first order differential equation as a function of the tracking error and subsequently combined with a QIH-NMPC algorithm for online updating of the unknown parameter. The effectiveness of the proposed control scheme is demonstrated on a continuous stirred tank reactor (CSTR) and an experimental cascaded three-tank system with uncertain model parameters, structural plant/model mismatch and noisy measurements. For the purpose of comparison, the state-of-the-art online state and parameter estimators such as moving horizon estimation (MHE) and extended Kalman filter (EKF) were also incorporated into QIH-NMPC algorithm. The simulation and experimental results obtained showed the efficacy of the proposed adaptation scheme as it demonstrated a comparable performance to standard estimators (MHE and EKF) although with a lesser computational time.
References
1.
Magni
,
L.
,
De Nicolao
,
G.
, and
Scattolini
,
R.
, 2001
, “
Output Feedback and Tracking of Nonlinear Systems With Model Predictive Control
,” Automatica
,
37
(10
), pp. 1601
–1607
.10.1016/S0005-1098(01)00102-92.
González
,
A. H.
,
Adam
,
E. J.
, and
Marchetti
,
J. L.
, 2008
, “
Conditions for Offset Elimination in State Space Receding Horizon Controllers: A Tutorial Analysis
,” Chem. Eng. Process.: Process Intensif.
,
47
(12
), pp. 2184
–2194
.10.1016/j.cep.2007.11.0113.
Maeder
,
U.
, and
Morari
,
M.
, 2010
, “
Offset-Free Reference Tracking With Model Predictive Control
,” Automatica
,
46
(9
), pp. 1469
–1476
.10.1016/j.automatica.2010.05.0234.
Rao
,
C. V.
, and
Rawlings
,
J. B.
, 1999
, “
Steady States and Constraints in Model Predictive Control
,” AIChE J.
,
45
(6
), pp. 1266
–1278
.10.1002/aic.6904506125.
Muske
,
K. R.
, and
Badgwell
,
T. A.
, 2002
, “
Disturbance Modeling for Offset-Free Linear Model Predictive Control
,” J. Process Control
,
12
(5
), pp. 617
–632
.10.1016/S0959-1524(01)00051-86.
Pannocchia
,
G.
, and
Rawlings
,
J. B.
, 2003
, “
Disturbance Models for Offset-Free Model Predictive Control
,” AIChE J.
,
49
(2
), pp. 426
–437
.10.1002/aic.6904902137.
Pannocchia
,
G.
, 2003
, “
Robust Disturbance Modeling for Model Predictive Control With Application to Multivariable Ill-Conditioned Processes
,” J. Process Control
,
13
(8
), pp. 693
–701
.10.1016/S0959-1524(02)00134-88.
Pannocchia
,
G.
, and
Bemporad
,
A.
, 2007
, “
Combined Design of Disturbance Model and Observer for Offset-Free Model Predictive Control
,” IEEE Trans Autom. Control
,
52
(6
), pp. 1048
–1053
.10.1109/TAC.2007.8990969.
Huang
,
R.
,
Patwardhan
,
S. C.
, and
Biegler
,
L. T.
, 2009
, “
Robust Extended Kalman Filter Based Nonlinear Model Predictive Control Formulation
,” 48th IEEE Conference on Decision and Control Held Jointly With 2009 28th Chinese Control Conference
, IEEE, Shanghai, China, Dec. 15–18, pp. 8046
–8051
.10.1109/CDC.2009.540042110.
Huang
,
R.
,
Biegler
,
L. T.
, and
Patwardhan
,
S. C.
, 2010
, “
Fast Offset-Free Nonlinear Model Predictive Control Based on Moving Horizon Estimation
,” Ind. Eng. Chem. Res.
,
49
(17
), pp. 7882
–7890
.10.1021/ie901945y11.
Park
,
B. J.
,
Kim
,
Y.
, and
Lee
,
J. M.
, 2021
, “
Design of Switching Multilinear Model Predictive Control Using Gap Metric
,” Comput. Chem. Eng.
,
150
, p. 107317
.10.1016/j.compchemeng.2021.10731712.
Meadows
,
E.
, and
Rawlings
,
J. B.
, 1997
, “
Model Predictive Control
,” Nonlinear Process Control
,
M.
Henson
and
D. H.
Seborg
,
Prentice Hall
,
Upper Saddle River, NJ
, pp. 233
–310
.13.
Bequette
,
B. W.
, 2007
, “
Non-Linear Model Predictive Control, a Personal Retrospective
,” Can. J. Chem. Eng.
,
85
(4
), pp. 408
–415
.10.1002/cjce.545085040314.
Patwardhan
,
A. A.
,
Rawlings
,
J. B.
, and
Edgar
,
T. F.
, 1990
, “
Nonlinear Model Predictive Control
,” Chem. Eng. Commun.
,
87
(1
), pp. 123
–141
.10.1080/0098644900894068715.
Lee
,
J. H.
, and
Ricker
,
N. L.
, 1994
, “
Extended Kalman Filter Based Nonlinear Model Predictive Control
,” Ind. Eng. Chem. Res.
,
33
(6
), pp. 1530
–1541
.10.1021/ie00030a01316.
Huang
,
R.
,
Patwardhan
,
S. C.
, and
Biegler
,
L. T.
, 2012
, “
Robust Stability of Nonlinear Model Predictive Control Based on Extended Kalman Filter
,” J. Process Control
,
22
(1
), pp. 82
–89
.10.1016/j.jprocont.2011.10.00617.
Morari
,
M.
, and
Maeder
,
U.
, 2012
, “
Nonlinear Offset-Free Model Predictive Control
,” Automatica
,
48
(9
), pp. 2059
–2067
.10.1016/j.automatica.2012.06.03818.
Caspari
,
A.
,
Djelassi
,
H.
,
Mhamdi
,
A.
,
Biegler
,
L. T.
, and
Mitsos
,
A.
, 2021
, “
Semi-Infinite Programming Yields Optimal Disturbance Model for Offset-Free Nonlinear Model Predictive Control
,” J. Process Control
,
101
, pp. 35
–51
.10.1016/j.jprocont.2021.03.00519.
Das
,
B.
, and
Mhaskar
,
P.
, 2015
, “
Lyapunov-Based Offset Free Model Predictive Control of Nonlinear Process Systems
,” Can. J. Chem. Eng.
,
93
(3
), pp. 471
–478
.10.1002/cjce.2213420.
Tatjewski
,
P.
, and
Lawrynczuk
,
M.
, 2020
, “
Algorithms With State Estimation in Linear and Nonlinear Model Predictive Control
,” Comput. Chem. Eng.
,
143
, p. 107065
.10.1016/j.compchemeng.2020.10706521.
Rangaiah
,
G. P.
,
Saha
,
P.
, and
Tade
,
M. O.
, 2002
, “
Nonlinear Model Predictive Control of an Industrial Four-Stage Evaporator System Via Simulation
,” Chem. Eng. J.
,
87
(3
), pp. 285
–299
.10.1016/S1385-8947(01)00240-622.
Lakshmi Narayanan
,
N. R.
,
Krishnaswamy
,
P. R.
, and
Rangaiah
,
G. P.
, 1997
, “
An Adaptive Internal Model Control Strategy for pH Neutralization
,” Chem. Eng. Sci.
,
52
(18
), pp. 3067
–3074
.10.1016/S0009-2509(97)00130-923.
Hu
,
Q.
, and
Rangaiah
,
G. P.
, 1999
, “
Adaptive Internal Model Control of Nonlinear Processes
,” Chem. Eng. Sci.
,
54
(9
), pp. 1205
–1220
.10.1016/S0009-2509(98)00543-024.
Shukla
,
N. V.
,
Deshpande
,
P. B.
,
Ravi Kumar
,
V.
, and
Kulkarni
,
B. D.
, 1993
, “
Enhancing the Robustness of Internal Model Based Nonlinear pH Controller
,” Chem. Eng. Sci.
,
48
(5
), pp. 913
–920
.10.1016/0009-2509(93)80329-O25.
Al Seyab
,
R. K. S.
, 2006
, Nonlinear Model Predictive Control Using Automatic Differentiation
,
Cranfield University, Cranfield, UK
.26.
Ebirim
,
K. U.
,
Lecchini-Visintini
,
A.
,
Rubagotti
,
M.
, and
Prempain
,
E.
, 2023
, “
Constrained Model Predictive Control With Integral Action for Twin Rotor MIMO Systems
,” ASME J. Dyn. Syst. Meas. Contr.
,
145
(8
), p. 081006
.10.1115/1.406273527.
Adetola
,
V.
,
DeHaan
,
D.
, and
Guay
,
M.
, 2009
, “
Adaptive Model Predictive Control for Constrained Nonlinear Systems
,” Syst. Control Lett.
,
58
(5
), pp. 320
–326
.10.1016/j.sysconle.2008.12.00228.
Adetola
,
V.
, and
Guay
,
M.
, 2011
, “
Robust Adaptive MPC for Constrained Uncertain Nonlinear Systems
,” Int. J. Adapt. Control Signal Process.
,
25
(2
), pp. 155
–167
.10.1002/acs.119329.
Jabarivelisdeh
,
B.
,
Carius
,
L.
,
Findeisen
,
R.
, and
Waldherr
,
S.
, 2020
, “
Adaptive Predictive Control of Bioprocesses With Constraint-Based Modeling and Estimation
,” Comput. Chem. Eng.
,
135
, p. 106744
.10.1016/j.compchemeng.2020.10674430.
Dutta
,
L.
, and
Das
,
D. K.
, 2021
, “
An Adaptive Feedback Linearized Model Predictive Controller Design for a Nonlinear Multi-Input Multi-Output System
,” Int. J. Adapt. Control Signal Process.
,
35
(6
), pp. 991
–1016
.10.1002/acs.323931.
Pipino
,
H. A.
,
Cappelletti
,
C. A.
, and
Adam
,
E. J.
, 2021
, “
Adaptive Multi-Model Predictive Control Applied to Continuous Stirred Tank Reactor
,” Comput. Chem. Eng.
,
145
, p. 107195
.10.1016/j.compchemeng.2020.10719532.
Mayne
,
D. Q.
,
2014
, “
Model Predictive Control: Recent Developments and Future Promise
,” Automatica
,
50
(12
), pp. 2967
–2986
.10.1016/j.automatica.2014.10.12833.
Pistikopoulos
,
E. N.
,
Barbosa-Povoa
,
A.
,
Lee
,
J. H.
,
Misener
,
R.
,
Mitsos
,
A.
,
Reklaitis
,
G. V.
,
Venkatasubramanian
,
V.
, et al., 2021
, “
Process Systems Engineering –The Generation Next?
,” Comput. Chem. Eng.
,
147
, p. 107252
.10.1016/j.compchemeng.2021.10725234.
Mayne
,
D.
,
2013
, “
An Apologia for Stabilising Terminal Conditions in Model Predictive Control
,” International Journal of Control
,
86
(11
), pp. 2090
–2095
.10.1080/00207179.2013.81364735.
Chen
,
H.
, and
Allgower
,
F.
, 1998
, “
A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme With Guaranteed Stability
,” Automatica
,
34
(10
), pp. 1205
–1217
.10.1016/S0005-1098(98)00073-936.
Findeisen
,
R.
,
Imsland
,
L.
,
Allgower
,
F.
, and
Foss
,
B. A.
, 2003
, “
State and Output Feedback Nonlinear Model Predictive Control: An Overview
,” Eur. J. Control
,
9
(2–3
), pp. 190
–206
.10.3166/ejc.9.190-20637.
Das
,
B.
, and
Mhaskar
,
P.
, 2017
, “
Adaptive Output-Feedback Lyapunov-Based Model Predictive Control of Nonlinear Process Systems
,” Int. J. Robust Adaptive control.
,
28
(5
), pp. 1597
–1609
.10.1002/rnc.397338.
Rajhans
,
C.
,
Patwardhan
,
S. C.
, and
Pillai
,
H.
, 2017
, “
Discrete Time Formulation of Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme With Guaranteed Stability
,” IFAC-PapersOnLine
,
50
(1
), pp. 7181
–7186
.10.1016/j.ifacol.2017.08.60239.
Rajhans
,
C.
,
Griffith
,
D. W.
,
Patwardhan
,
S. C.
,
Biegler
,
L. T.
, and
Pillai
,
H. K.
, 2019
, “
Terminal Region Characterization and Stability Analysis of Discrete Time Quasi-Infinite Horizon Nonlinear Model Predictive Control
,” J. Process Control
,
83
, pp. 30
–52
.10.1016/j.jprocont.2019.08.00240.
Faanes
,
A.
, and
Skogestad
,
S.
, 2005
, “
Offset-Free Tracking of Model Predictive Control With Model Mismatch. experimental Results
,” Ind. Eng. Chem. Res.
,
44
(11
), pp. 3966
–3972
.10.1021/ie049422y41.
Huberman
,
B. A.
, and
Lumer
,
E.
, 1990
, “
Dynamics of Adaptive Systems
,” IEEE Trans. Circuits Syst.
,
37
(4
), pp. 547
–550
.10.1109/31.5275942.
Slotine
,
J.-J. E.
, and
Li
,
W.
, 2008
, Applied Nonlinear Control
,
Prentice Hall
,
Eaglewood Cliffs, NJ
.43.
Allgower
,
F.
,
Badgwell
,
T. A.
,
Qin
,
J. S.
,
Rawlings
,
J. B.
, and
Wright
,
S. J.
, 1999
, “
Nonlinear Predictive Control and Moving Horizon Estimation – An Introductory Overview
,” Advances in Control, Highlights of ECC-99
,
P. M.
Frank
, Hrsg.,
Springer
, Berlin, pp. 391
–449
.44.
Hicks
,
G. A.
, and
Ray
,
W. H.
, 1971
, “
Approximation Methods for Optimal Control Synthesis
,” Can. J. Chem. Eng.
,
49
(4
), pp. 522
–528
.10.1002/cjce.545049041645.
Qu
,
C. C.
, and
Hahn
,
J.
, 2009
, “
Computation of Arrival Cost for Moving Horizon Estimation Via Unscented Kalman Filtering
,” J. Process Control
,
19
(2
), pp. 358
–363
.10.1016/j.jprocont.2008.04.00546.
Zang
,
Z. J.
, and
Sugiura
,
H.
, 2017
, “
Robust Nonlinear Control of a Three-Tank System in the Presence of Mismatched Uncertainties
,” IFAC PapersOnline
,
50
, pp. 4048
–4093
.10.1016/j.ifacol.2017.08.79347.
Bamimore
,
A.
,
Osinuga
,
A. B.
,
Olaleke
,
M.
,
Adeniran
,
O.
,
Odunsi
,
O.
,
Salaudeen
,
A.
,
Owolabi
,
O. K.
, et al., 2020
, “
Design, Fabrication and Interfacing of Cascaded Three Tank System With Microcontroller Board for Research and Education in Process Control
,” Innovative Solution Eng.
,
3
(1
), pp. 12
–22
.48.
Multi Tank | INTECO
, 2009
, “
On Internet
,” accessed January 12, 2022, https://www.inteco.com.pl/products/multi-tank/.49.
Bamimore
,
A.
,
Osinuga
,
A. B.
,
Kehinde-Abajo
,
T. E.
,
Osunleke
,
A. S.
, and
Taiwo
,
O.
, 2021
, “
A Comparison of Two Artificial Neural Networks for Modeling and Predictive Control of a Cascaded Three-Tank System
,” IFAC-PapersOnLine
,
54
(21
), pp. 145
–150
.10.1016/j.ifacol.2021.12.025Copyright © 2023 by ASME
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